NONLINEAR DYNAMICAL APPROACH AND SELF-EXCITING THRESHOLD MODEL IN FORECASTING DAILY STREAM-FLOW

In the present study, forecasting performances of a nonlinear dynamical approach and a self-exciting threshold model were compared in daily stream-flow observed in No En River, USA. As a nonlinear dynamical approach, the k-nearest neighbour (k-NN) method with arithmetic average was applied. For the k-NN model, optimal embedding dimension was found with the correlation integral analysis. The correlation dimension of the runoff series was obtained as 2.89, and the first integer above this value was taken as embedding dimension (m=3). With these parameters, the k-NN's prediction performance was calculated for different neighbour numbers (k), and the best result was obtained for k=7. The SETAR models were constructed according to the Tsay's algorithm, and the best model was determined with different efficiency criteria and the best model's (SETAR (2,3,2)) prediction performance was compared with that of the k-NN. The results showed that the SETAR (2,3,2) model better forecasted the peak flows and low flow dynamics than the k-NN model. However, the k-NN model gave results that are more realistic after peak flow predictions that can be said the k-NN model is better in representation of nonlinear behavior of falling limb. Overall, in a relatively short data set, the performance indicators showed that the SETAR model's predictions are better than that of the k-NN model.